论文标题
使用git和量化消失
Bott vanishing using GIT and quantization
论文作者
论文摘要
如果$ω_y^j \ otimes l $对于每个$ j $和每个充分的线条捆绑$ l $都没有更高的共同体，则据说平滑的投射品种$ y $可以满足剂量消失。众所周知，很少有例子可以满足这一属性。其中包括托塔罗最近显示的感谢您的品种以及五重的Del Pezzo表面。在这里，我们提出了一个满足Bott Vanishing的新品种，即通过$ PGL_2 $的作用，在特征零的代数封闭字段上，$（\ Mathbb {p}^1）^n $的稳定git商。为此，我们使用Halpern-Leistner在GIT商的派生类别中所做的工作以及他的量化定理版本。我们还看到，使用类似的技术，我们可以为复曲案例恢复剂量消失。
A smooth projective variety $Y$ is said to satisfy Bott vanishing if $Ω_Y^j\otimes L$ has no higher cohomology for every $j$ and every ample line bundle $L$. Few examples are known to satisfy this property. Among them are toric varieties, as well as the quintic del Pezzo surface, recently shown by Totaro. Here we present a new class of varieties satisfying Bott vanishing, namely stable GIT quotients of $(\mathbb{P}^1)^n$ by the action of $PGL_2$, over an algebraically closed field of characteristic zero. For this, we use the work done by Halpern-Leistner on the derived category of a GIT quotient, and his version of the quantization theorem. We also see that, using similar techniques, we can recover Bott vanishing for the toric case.
